It could be heat rash? Our human son gets these. We changed his shampoo and for two months he would get heat rash eveytime he got sweaty. Then some folks suggested I give him a vinegar bath, and then I changed his shampoo. Needless to say, he is much better now, but he still gets a little bit red and bumpy if he is too hot, but nothing like before.
So my point- is yes it could be allergy related, as my son was hghly allergic to that shampoo....